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10.29.2012

I started a new unit in Geometry- Parallel and Perpendicular Lines. I started with a card sort. I numbered the back of the page going across 1-12. Then I copied each page on a different color of card stock and cut those in half. I passed it out to the students and had them cut out the individual squares. (Yay for student labor!) Unfortunately, when they cut, the numbers were cut in half which posed some problems. Maybe you should have students number them after they cut? Not sure what happened on my end.

I asked students to sort into groups. Some students sorted the ones with fractions, parentheses, and neither. I'm sure you will see a wide variation. The first hint I gave was that students should have three groups. They resorted and I went back around the room to observe. Next, I told them they would have one group of six and two groups of three. From here, almost everyone had their cards in the correct group.

I displayed this slide to make sure everyone had the correct groups.

A few students recognized that the one group of six were in slope-intercept form. Yay for Algebra I. I asked them to put those six cards back into their envelope. Then I passed out this worksheet and asked students to write in the equations on the cards onto the worksheet and solve for y. They did okay at this. After they were done I told them to get the six back out of the envelope because these were the answers to the top of their worksheet. See what I did there?

From there we went to the bottom half of the worksheet which was graphing lines on the calculator. Then on the back we worked down each column individually. We solved a pair of equations for y. We graphed. We noticed both lines were parallel. We compared the equations. Oh my, they have the same slope! We did this three times and summarized that all parallel lines must have the same slope.

10.27.2012

She is really, really good. Other than our type A personalities, we don't really have a lot in common. She is a beauty pageant queen many times over, perfect teeth, really tiny, voluminous hair, extra peppy, loves small talk, and very friendly. I'm not any of those things. She's definitely smarter than me when it comes to math.

She has her stuff together. In some ways, I feel like we are on the same level and consequently, I have really high expectations for her. She taught my Algebra I class all week and just modified my materials. The students could not believe this was the first time she's ever taught. When I observe her, I write two-column notes labeled "Go" and "Grow". That helps me balance my comments between praise and instruction. I am having a blast with 'coaching' her and just making suggestions. It's so much fun! If we could do this with teachers for a full year, there would be no stopping us. It is such a valuable process.

I like having someone to discuss and brainstorm ideas with and together we've made some changes to the pacing and created some activities. It's nice to not be so isolated. It's also nice to sit back and let someone else be in charge.

But my favorite thing of all is this...not once have I compared myself to her or wished that I was different. I am very happy being me and teaching the way that I teach. I have been surprised and found some good ideas while watching her but I'm actually feeling more and more satisfied with who I am as a teacher.

That may seem silly to you...why would I ever compare myself to someone who hasn't been a teacher yet? But I spent a lot of years in various parts of my life comparing myself, not measuring up, and wanting to be someone else. I still sometimes compare my teaching ability to you mad geniuses out there. But this year, I am just really satisfied with where I'm at and what I'm doing. I'm confident....solid.

Today I had to teach in Algebra I because she works on Fridays and I wondered if it would be weird since she has taken over the class. (Warning: Some lameness will appear shortly) But it was seriously like coming home. It just felt right and I was thinking "Yeah, these are my kids." It just felt so comfortable and the lesson went so smoothly...confirmation that I just might have a handle on this beast we call teaching.

I've rarely had this experience. I am able to admire traits about someone else without withoutwithout making myself feel bad for not having those traits. It is possible to lift up someone else without degrading yourself. It is possible to like myself more and more for just being me. It is possible for me to measure up and not find myself lacking.

10.22.2012

First, I made a very basic grade sheet for my students to keep track of their grades. I'm tired of looking it up over and over or seeing the looks on their faces when they realize I don't have every single one of their grades memorized...similar to the look they get when they realize I can do mental math. *gasp*

This is nothing fancy at all but maybe there is someone who can't figure out how to make tables yet, or who doesn't want my grade sheet but is now inspired to make their own, or who just happens to need this file on the exact day they read this post (love when that happens!).

Behold:

Now to my real creation. I loved Nora Oswald's post about a relations and functions foldable. I had just finished that in Algebra II and realized how nice a foldable would have been to tie all that information together. Since I am now teaching functions in Algebra I, I modified her foldable so that it works for our interactive student binders.

I typed in the main stuff (text stolen from Nora) so that the real work of the students is to create the examples and non-examples which to me, seems like the higher order thinking I want to accomplish. If you decide to use this, when you fold the top down, do not fold exactly in half. Instead only fold to the bottom of the dotted line. Then you have space to write the title and everything fits nicely.

The students also label the outside flaps, which are created by cutting on the top dotted lines only. This gets them thinking a bit because they have to decide the difference between each flap.

My student teacher is using this today in her first lesson so I will try to update my post later tonight with pictures and whatnot. She will be teaching domain and range so we went ahead and put those blanks on the foldable as well.

10.15.2012

I know other people have posted picture frame stations before but mine is a little different. I was teaching function composition in Algebra 2 and I started by making students wear function necklaces (nod to @jreulbach) and just working a lot of examples. I thought it would make a good visual of which function to evaluate first but I couldn't really keep talking about one boys function and putting it inside of another boy's function for very long...

The next day I set up function composition stations. I bought 5 x 7 plastic frames from Wal-Mart for $.95 each. I used big colored index cards to write the functions on. I gave students a worksheet that had four boxes per station. Two boxes were problems asking students to compose functions and write a new expression and the other two asked them to compose functions and evaluate for a number.

I varied them a bit, for example, an f of f, a station with three functions where they only used two at a time, etc.

I also bought tiny 3 x 5 frames and used 3 x 5 index cards (color coded to the big ones of course) and worked out each problem. The answer cards went inside the small frame which were neatly tucked inside the larger frame. I chose a leader for each station, based on who seemed to catch on the quickest during class the day before. Everyone worked the problem at the same time and then the leader would show the answer card and answer any questions.

The logistics worked okay but it didn't suit the concept too well; they're really struggling with it. I probably should have done some cut and paste activity where they literally replace....ooh I might just have planned tomorrow's lesson in my brain!

Anyway, two other things to share. One, I found this parent teacher conference rubric on Pinterest and minus the dorky school bus picture, you can use this for any content area and any age level. Yay.

Two, for my grad class I had to create an assessment plan so I thought I would share what I have. You can download my template or read mine and let it make you think a little more deeply about how often you are truly assessing.Original

Ok I'm back. I have alluded to different ideas in posts throughout the summer of more solid plans but this seems like a good time to explain.

Basically I used the feedback from that post and formed a new idea.

Jason comments:
I'd suggest that the warm up should be something that all kids can do
with minimal guidance from the you. There should be (virtually) no
(mathematical) barrier to entry. The last thing you want to have to do
is to reteach/tutor while you are trying to take role, get kids settled
in, etc. Think of it as time to build procedural fluency and
automaticity.

Excellent thinking.

DKlemme comments:
At the Minnesota Math Conf. I saw some warm ups that interested me. 2
week cycles of questions, 3 review type questions of past material or
skills needed for next concept. Use of vocab in directions, as the
cycle gets into week two you take out the key vocab and Ss fill it in.

Also excellent thinking.

I combined those two ideas together and made a PowerPoint of pre-algebra skills, mostly three questions a piece, for three days a week of the entire school year (the fourth day is a practice quiz and the fifth day is a school thing). In the first half the questions go through a 2 week cycle where the first week contains hints and the second week does not. I use this PowerPoint for all my classes Alg I - Alg II because they all need refreshers and hopefully can at least start on the problems without me.

Creating that PowerPoint was a godsend although it took me hours and hours and I temporarily hated my life while doing it. But I always have a way to start class smoothly and it gives me a couple of minutes to get my stuff together. Oh, and I've been using blank quarter sheets of copy paper by the door that kids just grab on their way in. I told them at the beginning that I may or may not collect them and some students choose to keep them even when I tell them to throw them away. Truthfully, I've only collected them once. I've had a few issues with students not wanting to do them, especially since I don't grade them, but it's pretty hard for them to refuse when I stand beside their desk and ask them if they will do these problems for me. Overall I've had a very positive reaction.

As for exit slips....they died on the table. In a later post I briefly mentioned exit slips in my new beginnings and then proceeded to talk way more about summarizing. I've been using that more as a way of summarizing the lesson and getting feedback rather than an exit slip. I built this right in to the guided notes- after almost every example I force students to stop and write in words what we just did. I think it's been a really good idea and I hope that it has started to build the habit of frequently stopping and thinking about what we're doing as well as putting it into words. I don't really have any hard facts to support my thinking but I know that in review games and on assessments I have been asking students to explain, tell the difference, write examples, write analogies, etc and they haven't balked yet. I would say that's an improvement.

I had mentioned unit summaries which morphed into my PEEL graphic organizer but that just took way too much time and has since fell by the wayside.

The quarter ends this week so I'm thinking of trying something new. Since we made a summaries tab in our math binders, I've got to use that for something. I'd like to try Nora Oswald's Learning Log Prompts Poster. I could modify my original unit summary sheet to work for this where students write the date, the concept taught, and then answer one of the prompts. Actually, the more I think about that, the more I really like the idea.

That will be another good habit to get into and something I could use after the bell ringer to promote some discussion: turn to your partner and share what you wrote at the end of class yesterday. I don't know, that will probably take up too much time but you never know when you will need a time filler.

All in all, I'm satisfied with my bell ringer and I'm happy with how often we are summarizing- I guess if I can get this exit slip idea nailed down then I'll be all good.

Thanks mrsaitoromath for motivating me to write this blog post- you've reminded me of something I could be doing better.

I displayed this slide with key words in it and we wrote them in the correct places.

I like the idea of keeping this all year and adding more words to it as we come across them. Here's the download:

In Algebra II we made a foldable for Operations with Functions. On the outside flaps we wrote how to do each operation and things to remember (i.e. don't add exponents when combine like terms).

We made this after I taught those concepts so I had students go back to their notes and pick out two examples of each to write on the inside. Just one small way to show that our notes have a purpose. Here's the download:

If you notice, function composition is on here as well. I haven't taught it yet but I noticed when I folded the foldable, the back was split up nicely into four squares as well. I threw the title on there and now we can add to that this week.

10.05.2012

I was asked to share a "My Favorite" at this week's #globalmath department. I wanted to share something new that I hadn't blogged about yet but now I also get to blog about something new!

This idea kind of came out of nowhere but is really a mix of the mistake game and error analysis.

In Algebra I we were working on translating word problems into an inequality to solve and graph. A student had volunteered to work the problem on the board and had set it up correctly but was solving it all kinds of wrong.

The other students began glancing around and whispering back and forth because they could see her errors too. I thought to myself, how can I correct her without making her feel stupid in front of the class?

I told the students that if they saw any mistakes in her work that they must ask her a question rather than make a comment. I told them that saying "You're wrong or you messed up" is not helpful.

I felt like I could literally see the wheels turning in their brain as they thought about how to phrase their observations into a question. I guided them by telling them they could start their question with "Why did you ________?" or "Couldn't you __________?"

As they started to ask questions, the student realized her own mistake, corrected it and explained "Oh, I should have ___________". The students picked this up easily and it has become a powerful tool. I'm trying to structure every piece of feedback I give as a question.

I feel pretty good about the questions I ask during a lesson but now as students are working and asking for help, I avoid telling them right or wrong, yes or no, but phrase every comment as a question.

For example:

Did you find what the question is asking for?

What do you think?

If I tell you that you are wrong, what would you change?

Is x alone?

Is that your final answer?

Does it make sense to do it that way?

What is another way you could do it?

Do you notice a pattern?

Do your partners agree?

At the end, I debriefed by asking students why I made them ask questions rather than comments. Their response was that telling someone they are wrong doesn't tell them where they went wrong or how to fix it. Bazinga!

I find that the more often I ask students why I do something, the more I learn about my teaching style and my instructional choices. Sometimes what appears natural to a teacher needs some concrete student reasoning behind it. They always give me better answers than I think of on my own. It never hurts to let students give purpose to what happens in the classroom.

When everyone has completed 1 problem – they compare answers – to
determine which is correct and will be used for the group answer.

All team members run over to teacher. Teacher checks solution:

If correct, hole punch the outer edge of the problem, students return to work space and continue to next problem.

If incorrect, they return to workspace and rework.

She also suggested staggering which # each team begins working on.

The teacher who shared said this accomplishes 3 things:

Students must talk / agree on a solution.

Students are physically up and moving.

Sure you could put a check mark, stamp it, etc. but the sound /
click of the hole – punch (or stapler) does something crazy and the
students - especially for those who are struggling are motivated to keep
on working. Weird, huh?

There are two pages and a total of 16 problems.

In Pam's same post, she mentions Mrs. H's Ghosts in the Graveyard review game. So I kinda stole that for the next concept review of writing domain and range in set and interval notation. But, I decided to modify it since Halloween is still far off. Fortunately for me, Columbus day is right around the corner of the weekend which means I created....

1. Divide class into groups of 3-4 students
2. Give each group a problem card
3. Every member of the group works the problem and raises their hand
when they are done. You go over and check their work and answers. If
EVERYONE has done the problem correctly, they get a "little ghost" which
they put their group number on and hang in any one of the graveyards.
4. As they finish a "Problem Card", they go get another one. The goal
is get as many "little ghosts" as possible to hang in the graveyards.
5. About 10 minutes before the end of the period, I draw for how many
points each graveyard will be worth. I use 0, 25, 50, 75, and 100. So
if graveyard 2 is worth 50 points and a group had 2 ghosts in that
graveyard, they will get 100 points.
6. Tally all the points for the groups and give prizes to 1st and 2nd.

Since I made ships in the ocean, I will be naming all 5 oceans rather than graveyards....how perfect!

The above document has mini sailboats at the bottom but I later decided I wanted ships in color that I could laminate and reuse so this is my second sheet of ships (say that 5 times fast) that I like even better. Everybody needs a little pirate...or a big one.

I'm thinking that I will probably blog these two games again separately so I can add in pictures and notes about how the game went during class.